Difference between revisions of "Chi"
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File:Coshintegral.png|Graph of $\mathrm{chi}$ on $(0,5]$. | File:Coshintegral.png|Graph of $\mathrm{chi}$ on $(0,5]$. | ||
| − | File:Domain coloring hyperbolic cosine integral.png|[[Domain coloring]] of [[analytic continuation]] of $\ | + | File:Domain coloring hyperbolic cosine integral.png|[[Domain coloring]] of [[analytic continuation]] of $\mathrm{chi}$. |
</gallery> | </gallery> | ||
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<center>{{:*-integral functions footer}}</center> | <center>{{:*-integral functions footer}}</center> | ||
Revision as of 18:43, 25 July 2015
The hyperbolic cosine integral $\mathrm{chi} \colon (0,\infty) \rightarrow \mathbb{R}$ is defined by the formula $$\mathrm{chi}(z)=\gamma + \log(z) + \displaystyle\int_0^z \dfrac{\mathrm{cosh}(t)-1}{t} dt,$$ where $\gamma$ denotes the Euler-Mascheroni constant, $\log$ denotes the logarithm, and $\mathrm{cosh}$ denotes the hyperbolic cosine function.
- Coshintegral.png
Graph of $\mathrm{chi}$ on $(0,5]$.
Domain coloring of analytic continuation of $\mathrm{chi}$.
